结构随机分析的Monte Carlo加权残值法

本文提出一种结构随机分析的Monte Carlo加权残值法。文中建立了这种方法的基本列式,并通过静力挠度、固有频率和屈曲荷载等算例,表明本文方法理论简捷,计算工程量少,精度较高,是随机结构数值分析的有效方法。     

Fokker-Planck方程有限解析/Monte Carlo数值模拟方法

对白噪声驱动随机系统的Fokker-Planck方程进行约化，求得约化方程的解析解，使 用局部解析解和Monte Carlo结合方法求解常系数Fokker-Planck方程，并与常系数Fokker-Planck方程的精确解 进行对比，之后求解了变驱动力系统的行为. 数值模拟结果表明，有限解析/Monte Carlo结合的方法，能成功求解一维Fokker-Planck方程，求解粒子数为10$^{5}$个，能获得 十分光滑的PDF分布曲线，计算颗粒在300个时，就能获得较好的均值. 其研究为两相 湍流PDF模型新计算方法研究提供基础.     

基于Monte Carlo模拟的砂土液化评估研究

探讨了MonteCarlo模拟方法用于砂土液化势评估的基本原理和过程, 建立了评判砂土液化的随机模拟模型和概率分布函数, 以及随机模拟的流程框图。     

考虑颗粒间碰撞的气固两相流拉格朗日模拟

在均匀,稳定的各向同性气固两相紊流场颗粒弥散的拉格朗日模拟计算方法基础上,进一步考虑了流场中颗粒之间的碰撞对于模拟计算结果的影响。与Lavieville用大涡模拟所做的计算结果进行了对比,以对本方法进行验证,并考察了颗粒间的碰撞分别对流体相和颗粒相的影响。     

快速颗粒流碰撞应力的动理模型

颗粒碰撞是快速颗粒流的动量传递,能量传递及耗散的主要机制。因此,碰撞应力是快速颗粒流研究的主要内容。本文基于大小均匀、光滑圆球颗粒的非弹性碰撞模型,类比气体分子动理论中的处理方法得出快速颗粒流积分形式的碰撞应力,能量传递通量及能量耗散率等关系。在颗粒速度分布函数的一级近似式符合Maxwell分布的假设下,对碰撞应力积分得出相应于Boltzmann方程二级近似解的碰撞应力表达式。在简单快速颗粒流动条件下,本文的理论结果与实验资料符合较好。     

基于Monte Carlo方法的磁驱动准等熵压缩实验不确定度量化评估

磁驱动准等熵压缩实验是研究材料偏离Hugoniot状态高压物性和动力学行为的重要实验技术之一,开展不确定量化评估具有重要意义和价值。基于Monte Carlo原理,结合磁驱动准等熵压缩实验过程分析、Lagrange分析和特征线正向数据处理方法建立了适用于此类实验的Monte Carlo不确定度量化评估方法,实现利用磁驱动准等熵压缩实验获取材料声速、应力、应变等物理量以及状态方程和本构关系等物理模型的不确定度量化评估。利用建立的不确定度评估方法,对文献中已开展的钽、铜和NiTi合金的磁驱动准等熵压缩实验结果进行不确定度量化评估与分析。结果表明,基于本文中方法的评估结果与国外文献以相同原理得到的评估结果一致。对基于CQ-4装置开展的NiTi合金磁驱动准等熵压缩实验的评估结果表明,设计的磁驱动准等熵压缩实验是一种可靠的精密物理实验。在此基础上,深入讨论了磁驱动准等熵压缩实验的误差相关性和敏感性。结果表明：台阶样品厚度和粒子速度的测量是影响实验精度的主要因素。     

气固两相流中颗粒碰撞的Monte-Carlo数值模拟

利用颗粒碰撞动力学模型和颗粒几何碰撞率模型,采用Monte—Carlo算法来模拟颗粒之间碰撞,把该算法与求解雷诺应力-概率密度函数模型的有限差分-Monte Carlo算法耦合起来,对轴对称突扩通道内的两相旋流场进行了数值模拟,模拟结果表明,由于颗粒碰撞使颗粒的动能和湍动能在三个坐标方向上进行了再分配,从而导致颗粒的动能和湍动能在三个坐标方向上趋于各向同性;另外,由于颗粒碰撞破坏了颗粒-颗粒、颗粒-流体微团之间的速度关联,从而造成颗粒湍动能及两相速度脉动关联的降低。     

基于碰撞模型的斜坡滚石颗粒速度预测

滑坡滚石灾害是西部山区常见的地质灾害类型,具有突发性和随机性强的特点,是山区地质灾害预测和防治工作的重点和难点.本文基于颗粒接触理论,考虑影响斜坡滚石碰撞过程中的随机因素,建立了用于预测斜坡滚石颗粒碰撞后速度的理论模型.根据冲量及冲量矩定理建立滚石颗粒碰撞基本方程,得到斜坡滚石颗粒碰撞后反弹速度的解析解.结果表明:斜坡滚石碰撞后反弹速度的解析解包含了坡角、坡体上被碰颗粒速度以及角度、入射速度和角度以及撞击角度等随机因素;当考虑入射滚石颗粒与坡体上被碰颗粒的撞击角度变化时,模型预测结果与试验结果吻合较好;本文进一步预测了滚石颗粒碰撞后颗粒反弹线速度和角度以及反弹旋转角速度的概率分布情况.结果显示,反弹颗粒速度和角度以及反弹旋转角速度的概率分布均服从高斯分布;当坡体上被碰颗粒速度和坡角发生变化时,其对反弹颗粒速度和角度以及反弹旋转角速度概率分布定性上没有影响,但是对概率分布的中心参数有显著影响.     

颗粒群碰撞搜索及CFD-DEM耦合分域求解的推进算法研究

在采用计算流体力学-离散元耦合方法(computational fluiddynamics-discrete element method, CFD-DEM)进行固液两相耦合分析时, 颗粒计算时间步的选取直接影响到耦合计算精度和计算效率. 为此, 本文选取每个目标颗粒为研究对象, 引入插值函数计算时间步的运动位移, 构建可变空间搜索网格; 通过筛选可能碰撞颗粒建立搜索列表, 采用逆向搜索方式判断碰撞颗粒, 从而提出一种改进的DEM方法(modified discreteelement method, MDEM). 该算法在颗粒群与流体耦合计算中, 颗粒计算初始时间步选取不受颗粒碰撞时间限制, 通过自动调整和修正实现大步长, 由颗粒和流体耦合条件实时更新流体计算时间步, 使颗粒计算时间步选取过小导致计算效率低、选取过大导致颗粒碰撞漏判的问题得以解决, 为颗粒与流体耦合的数值模拟提供了行之有效的计算方法. 通过两个颗粒和多个颗粒的数值模拟, 得到的颗粒间碰撞力、碰撞位置及次数, 与理论计算结果的相对误差均低于2%, 与传统的DEM碰撞搜索算法相比, 在选取的3种计算时间步均不会影响计算精度, 且有较高的计算效率. 通过多个颗粒与流体的耦合数值模拟, 采用传统的CFD-DEM方法, 只有颗粒计算时间步选取10$^{-6}$ s或更小才能得到精确解, 而采用本文方法取10$^{-4}$ s也能够得到精确解, 避免了颗粒碰撞随时间步增大而出现的漏判问题, 且计算耗时降低了16.7%.      

基于碰撞模型的斜坡滚石颗粒速度预测

滑坡滚石灾害是西部山区常见的地质灾害类型,具有突发性和随机性强的特点,是山区地质灾害预测和防治工作的重点和难点. 本文基于颗粒接触理论,考虑影响斜坡滚石碰撞过程中的随机因素,建立了用于预测斜坡滚石颗粒碰撞后速度的理论模型. 根据冲量及冲量矩定理建立滚石颗粒碰撞基本方程,得到斜坡滚石颗粒碰撞后反弹速度的解析解. 结果表明:斜坡滚石碰撞后反弹速度的解析解包含了坡角、坡体上被碰颗粒速度以及角度、入射速度和角度以及撞击角度等随机因素;当考虑入射滚石颗粒与坡体上被碰颗粒的撞击角度变化时,模型预测结果与试验结果吻合较好;本文进一步预测了滚石颗粒碰撞后颗粒反弹线速度和角度以及反弹旋转角速度的概率分布情况. 结果显示,反弹颗粒速度和角度以及反弹旋转角速度的概率分布均服从高斯分布;当坡体上被碰颗粒速度和坡角发生变化时,其对反弹颗粒速度和角度以及反弹旋转角速度概率分布定性上没有影响,但是对概率分布的中心参数有显著影响.      

Multi-monte-carlo method for general dynamic equation considering particle coagulation

Introduction ParticulateMatter(PM10,aerodynamicdiameterlessthan10μm)hasbeenwidely investigated.Somekindsofcombustionincludingcoalcombustion,gasoline/dieseloil combustionofvehicle,municipalsolidwastecombustion,etc,areoneofthemainsourcesof PM10[1].Particle…     

各向同性湍流内颗粒碰撞率的直接模拟研究

对 Re_{\lambda } 约为51均匀各向同性湍流内 St_{k}(=\tau_{p}/\tau_{k}) 为 0 ~10.0 的 有限惯性颗粒的碰撞行为进行了直接数值模拟，以研究湍流对有限惯性 颗粒碰撞的影响. 结果表明，具有一定惯性颗粒的湍流碰撞率完全不同于零惯性的轻颗粒 (St_{k}=0) 和可忽略湍流作用的重颗粒 (St{k} \to \infty) , 其变化趋势极其复杂： 在Stk为 0~1.0 之间，颗粒的碰撞率随 St 的增加而近乎线性地剧烈增长，在 Stk≈1.0 3.0(对应的StE=τp/Te≈0.5)附近，颗粒碰撞率出现两个峰值，在Stk>3.0以后，颗粒的碰撞率随惯性增 大而逐渐趋向于重颗粒极限；在峰值处，有限惯性颗粒的平均碰撞率的峰值较轻颗粒增强了 30倍左右. 为进一步分析湍流作用下颗粒碰撞率的影响因素，分别使用可能发生碰撞 的颗粒对的径向分布函数和径向相对速度来量化颗粒的局部富集效应和湍流掺混效应，表明 St_{k} \approx 1.0 时局部富集效应最为强烈，使得颗粒的碰撞率出现第1个峰值； 湍流掺混效应则随着颗粒Stk的增大而渐近增大；局部富集和湍流掺混联合作用的结果， 使得颗粒碰撞率在 St_{k} \approx 3.0 附近出现另一个峰值.     

结构动力学修改重分析方法的发展

结构动力学修改重分析技术是结构／机械振动控制和动态特性设计与优化的重要理论工具，本文简要述评了一些主要的高效重分析计算方法的研究发展概况，其中侧重于摄动分析方法。最后简单介绍了这些重分析方法的若干重要应用领域。     

A Quasimolecular Approach for Discrete Study of Droplet Collision

A discrete numerical method based on a molecular approach has been used as an alternative technique for the study of liquid drop dynamics. The Weber number and the Impact number are found to be the key parameters that determine the outcome of collision of two liquid droplets. This study confirms the experimental fact that the number of daughter droplets resulting from the collision of two droplets increases with the Impact number for a large Weber number. The shapes of the droplets at different phases during collision are in accord with the experimental observation.     

Notes on Philosophy of the Monte Carlo Method

Some personal (and inevitably biased) thoughts pertinent to the Monte Carlo method are shared with the reader; in this mass production process of papers we are pausing and asking ourselves some nagging questions. Various aspects of the philosophy of the method are discussed. Its role in stochastic mechanics is elucidated and some questions are posed in view of promoting a further constructive discussion     

Collision between high and low viscosity droplets: Direct Numerical Simulations and experiments

Binary droplet collisions are of importance in a variety of practical applications comprising dispersed two-phase flows. In the present work we focus on the collision of miscible droplets, where one droplet is composed of a high viscous liquid and the other one is of lower viscosity. This kind of collisions take place in, for instance, spray drying processes when droplets with different solid content collide in recirculation zones. The aim of this paper is to investigate the details of the flow inside the colliding droplets. For this purpose, two prototype cases are considered, namely the collision of equal sized droplets and the collision between a small and highly viscous droplet and a bigger low viscous droplet. A new experimental method has been developed in order to visualize the penetration and mixing process of two colliding droplets, where a fluorescence marker is added to one liquid and the droplets are excited by a laser. The results show a delay in the coalescence which takes place during the initial stage of a collision of droplets with different viscosities. Direct Numerical Simulations based on the Volume-of-Fluid method are used to study these collisions and to allow for a more detailed inspection of the mixing process. The method is extended to consider a second liquid with a different viscosity. In order to reproduce the delay of coalescence, an algorithm for the temporal suppression of the coalescence is applied. A predictive simulation of the delay is not possible, because the extremely thin air gap separating the droplets cannot be resolved by the numerics. This approach is validated by comparison with experimental data. The results provide local field data of the flow inside the collision complex, showing in particular a pressure jump at the liquid–liquid interface although no surface tension is present. The detailed analysis of the terms in the momentum balance show that the pressure jump results from the viscosity jump at the liquid–liquid interface.     

Differentially weighted direct simulation Monte Carlo method for particle collision in gas–solid flows

In gas–solid flows, particle–particle interaction (typical, particle collision) is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles (e.g., agglomeration and fragmentation) in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo (DSMC) method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC (DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian–Lagrangian models for hydrodynamics. Three schemes (mass, momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.     

利用蒙特卡洛方法计算陶瓷刀具磨损可靠性

在连续切削条件下,陶瓷刀具的失效形式是以磨粒磨损为主的摩损失效,其磨损寿命由材料的断裂韧性、硬度和切削过程的参数决定,利用蒙特卡洛方法分别随机生成断裂韧性与硬度的样本值,利用连续车削试验确定切削过程参数,将得到的样本值与切削参数相结合可计算刀具在相应切削条件下的磨损寿命及其可靠性,计算结果表明：陶瓷刀具的断裂韧对磨损寿命的可靠性影响较为明显,因而可以利用断裂韧性来估算磨损可靠性。